Thinned completely random measures with applications in competing risks models

Abstract

We present a posterior analysis of kernel mixtures of thinned completely random measures (CRMs) for multivariate intensities, in the context of competing risks models. The construction of the thinned CRMs is derived from a common Poisson random measure that includes the thinning probabilities in its intensity and is transferable to existing Poisson partition calculus results for the posterior analysis (James (2002; Ann. Statist. 33 (2005) 1771–1799)). We derive the posterior thinned CRMs, provide generalizations of both the Blackwell and MacQueen Pólya urn formula and the (weighted) Chinese restaurant process for the variates and partitions generated from the thinned CRMs, and we outline strategies for the further development of Monte Carlo simulation for estimation.